Using these definitions, it seems obvious that they need not be applied together to an individual or group. The propensity for people to assume others beliefs based on one aspect of their personality seems to be a common trait in the human condition. (I know that I a guilty of this but I will admit this could be confirmation bias.) It suggests an oversimplification is made when assesing others when part of a group and leading to generalizations that fit the narritive already established by the one piece of information. This can be a useful shortcut in reasoning when the assumptions need to be grouped together to be true. Yet, without skeptical assesment, this shortcut becomes fallacious thinking.